Andrada Tatu

Quality Metrics in High-Dimensional Data Visualization: An Overview and Systematization

In this paper, we present a systematization of techniques that use quality metrics to help in the visual exploration of meaningful patterns in high-dimensional data. In a number of recent papers, different quality metrics are proposed to automate the demanding search through large spaces of alternative visualizations (e.g., alternative projections or ordering), allowing the user to concentrate on the most promising visualizations suggested by the quality metrics. Over the last decade, this approach has witnessed a remarkable development but few reflections exist on how these methods are related to each other and how the approach can be developed further. For this purpose, we provide an overview of approaches that use quality metrics in high-dimensional data visualization and propose a systematization based on a thorough literature review. We carefully analyze the papers and derive a set of factors for discriminating the quality metrics, visualization techniques, and the process itself. The process is described through a reworked version of the well-known information visualization pipeline. We demonstrate the usefulness of our model by applying it to several existing approaches that use quality metrics, and we provide reflections on implications of our model for future research.

Combining automated analysis and visualization techniques for effective exploration of high-dimensional data

Visual exploration of multivariate data typically requires projection onto lower-dimensional representations. The number of possible representations grows rapidly with the number of dimensions, and manual exploration quickly becomes ineffective or even unfeasible. This paper proposes automatic analysis methods to extract potentially relevant visual structures from a set of candidate visualizations. Based on features, the visualizations are ranked in accordance with a specified user task. The user is provided with a manageable number of potentially useful candidate visualizations, which can be used as a starting point for interactive data analysis. This can effectively ease the task of finding truly useful visualizations and potentially speed up the data exploration task. In this paper, we present ranking measures for class-based as well as non class-based Scatterplots and Parallel Coordinates visualizations. The proposed analysis methods are evaluated on different datasets.

A Taxonomy of Visual Cluster Separation Factors

We provide two contributions, a taxonomy of visual cluster separation factors in scatterplots, and an in‐depth qualitative evaluation of two recently proposed and validated separation measures. We initially intended to use these measures to provide guidance for the use of dimension reduction (DR) techniques and visual encoding (VE) choices, but found that they failed to produce reliable results. To understand why, we conducted a systematic qualitative data study covering a broad collection of 75 real and synthetic high‐dimensional datasets, four DR techniques, and three scatterplot‐based visual encodings. Two authors visually inspected over 800 plots to determine whether or not the measures created plausible results. We found that they failed in over half the cases overall, and in over two‐thirds of the cases involving real datasets. Using open and axial coding of failure reasons and separability characteristics, we generated a taxonomy of visual cluster separability factors. We iteratively refined its explanatory clarity and power by mapping the studied datasets and success and failure ranges of the measures onto the factor axes. Our taxonomy has four categories, ordered by their ability to influence successors: Scale, Point Distance, Shape, and Position. Each category is split into Within‐Cluster factors such as density, curvature, isotropy, and clumpiness, and Between‐Cluster factors that arise from the variance of these properties, culminating in the overarching factor of class separation. The resulting taxonomy can be used to guide the design and the evaluation of cluster separation measures.

Subspace search and visualization to make sense of alternative clusterings in high-dimensional data

In explorative data analysis, the data under consideration often resides in a high-dimensional (HD) data space. Currently many methods are available to analyze this type of data. So far, proposed automatic approaches include dimensionality reduction and cluster analysis, whereby visual-interactive methods aim to provide effective visual mappings to show, relate, and navigate HD data. Furthermore, almost all of these methods conduct the analysis from a singular perspective, meaning that they consider the data in either the original HD data space, or a reduced version thereof. Additionally, HD data spaces often consist of combined features that measure different properties, in which case the particular relationships between the various properties may not be clear to the analysts a priori since it can only be revealed if appropriate feature combinations (subspaces) of the data are taken into consideration. Considering just a single subspace is, however, often not sufficient since different subspaces may show complementary, conjointly, or contradicting relations between data items. Useful information may consequently remain embedded in sets of subspaces of a given HD input data space. Relying on the notion of subspaces, we propose a novel method for the visual analysis of HD data in which we employ an interestingness-guided subspace search algorithm to detect a candidate set of subspaces. Based on appropriately defined subspace similarity functions, we visualize the subspaces and provide navigation facilities to interactively explore large sets of subspaces. Our approach allows users to effectively compare and relate subspaces with respect to involved dimensions and clusters of objects. We apply our approach to synthetic and real data sets. We thereby demonstrate its support for understanding HD data from different perspectives, effectively yielding a more complete view on HD data.

Automated Analytical Methods to Support Visual Exploration of High-Dimensional Data

Visual exploration of multivariate data typically requires projection onto lower dimensional representations. The number of possible representations grows rapidly with the number of dimensions, and manual exploration quickly becomes ineffective or even unfeasible. This paper proposes automatic analysis methods to extract potentially relevant visual structures from a set of candidate visualizations. Based on features, the visualizations are ranked in accordance with a specified user task. The user is provided with a manageable number of potentially useful candidate visualizations, which can be used as a starting point for interactive data analysis. This can effectively ease the task of finding truly useful visualizations and potentially speed up the data exploration task. In this paper, we present ranking measures for class-based as well as non-class-based scatterplots and parallel coordinates visualizations. The proposed analysis methods are evaluated on different data sets.

ClustNails: Visual analysis of subspace clusters

Subspace clustering addresses an important problem in clustering multi-dimensional data. In sparse multi-dimensional data, many dimensions are irrelevant and obscure the cluster boundaries. Subspace clustering helps by mining the clusters present in only locally relevant subsets of dimensions. However, understanding the result of subspace clustering by analysts is not trivial. In addition to the grouping information, relevant sets of dimensions and overlaps between groups, both in terms of dimensions and records, need to be analyzed. We introduce a visual subspace cluster analysis system called ClustNails. It integrates several novel visualization techniques with various user interaction facilities to support navigating and interpreting the result of subspace clustering. We demonstrate the effectiveness of the proposed system by applying it to the analysis of real world data and comparing it with existing visual subspace cluster analysis systems.

Improving Projection-based Data Analysis by Feature Space Transformations

Generating effective visual embedding of high-dimensional data is difficult - the analyst expects to see the structure of the data in the visualization, as well as patterns and relations. Given the high dimensionality, noise and imperfect embedding techniques, it is hard to come up with a satisfactory embedding that preserves the data structure well, whilst highlighting patterns and avoiding visual clutters at the same time. In this paper, we introduce a generic framework for improving the quality of an existing embedding in terms of both structural preservation and class separation by feature space transformations. A compound quality measure based on structural preservation and visual clutter avoidance is proposed to access the quality of embeddings. We evaluate the effectiveness of our approach by applying it to several widely used embedding techniques using a set of benchmark data sets and the result looks promising.

Visualisierung und Analyse multidimensionaler Datensätze

ZusammenfassungFür multidimensionale Datensätze existieren eine Reihe von automatischen Analysemethoden und Visualisierungstechniken, um ihnen innewohnende Zusammenhänge und Charakteristika aufzudecken. Die zunehmende Größe und Komplexität solcher Daten macht es notwendig, beide Ansätze miteinander zu kombinieren. In diesem Artikel stellen wir Ihnen daher etablierte Methoden zur visuellen und zur automatischen Datenanalyse vor und zeigen neuere Ansätze auf, diese sinnvoll miteinander zu kombinieren. Dabei werden alle Erläuterungen anhand anschaulicher Beispiele verdeutlicht und so für den Leser nachvollziehbar.